Statistical equi-equal convergence of positive linear operators

Statistical equi-equal convergence of positive linear operators Positivity https://doi.org/10.1007/s11117-018-0588-z Positivity Statistical equi-equal convergence of positive linear operators 1 1 Fadime Dirik · Pınar Okçu Sahin ¸ Received: 14 February 2018 / Accepted: 22 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract Many researchers have been interested in the concept of statistical conver- gence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we define a new type of statistical convergence by using the notions of equi-statistical convergence and statis- tical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our definition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators. Keywords Statistical equal convergence · Equi-statistical convergence · Positive linear operators · Korovkin theorem · Modulus of continuity Mathematics Subject Classification 41A25 · 41A36 1 Introduction The notion of statistical convergence for sequences of real http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Statistical equi-equal convergence of positive linear operators

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-018-0588-z
Publisher site
See Article on Publisher Site

Abstract

Positivity https://doi.org/10.1007/s11117-018-0588-z Positivity Statistical equi-equal convergence of positive linear operators 1 1 Fadime Dirik · Pınar Okçu Sahin ¸ Received: 14 February 2018 / Accepted: 22 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract Many researchers have been interested in the concept of statistical conver- gence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we define a new type of statistical convergence by using the notions of equi-statistical convergence and statis- tical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our definition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators. Keywords Statistical equal convergence · Equi-statistical convergence · Positive linear operators · Korovkin theorem · Modulus of continuity Mathematics Subject Classification 41A25 · 41A36 1 Introduction The notion of statistical convergence for sequences of real

Journal

PositivitySpringer Journals

Published: Jun 2, 2018

References

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